1.

`{:("If",a = 1 + 2 + 4 + ..."to n terms"),(,b = 1 + 3 + 9 + ..."to n terms"),(,c =1 + 5 + 25+ ..."to n terms"):}` then `|(a,2b,4c),(2,2,2),(2^(n),3^(n),5^(n))|=`A. `30^(n)`B. `10^(n)`C. 0D. `2^(n) + 3^(n) + 5^(n)`

Answer» Correct Answer - C
We have,
`{:(a = 1 + 2 + 4,..."to n terms",= 2^(n) -1),(b = 1+ 3 + 9 +,..."to n terms",= (1)/(2) (3^(n) -1)),(c =1 + 5 + 25 +,..."to n terms",= (1)/(4) (5^(n) -1)):}`
`:. |(a,2b,4c),(2,2,2),(2^(n),3^(n),5^(n))|`
`= |(2^(n) -1,3^(n) -1,5^(n) -1),(2,2,2),(2^(n),3^(n),5^(n))|`
`= 2 |(2^(n) -1,3^(n) -1,5^(n) -1),(1,1,1),(1,1,1)|` Applying `R_(3) rarr R_(3) - R_(1)` and taking 2 common `R_(2)
`=2 xx 0 = 0`


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